In the recent literature, the Poisson distribution has been used to model COVID-19 death counts. Valid...

Transcribed Image Text:

In the recent literature, the Poisson distribution has been used to model COVID-19 death counts. Valid estimation of the death rate relies on the availability of accurate data on COVID-19 death counts. In some regions in the world, the accuracy of reported COVID-19 death counts is questionable. We are going to build a Bayesian model to estimate the death rate parameter due to COVID-19 using a Poisson sampling model but also allow for possible under-reporting of death counts. Let y₁, yn be the reported daily death counts for Region A for n different days. Let Z₁, Zn be the true (unreported) death counts, the sampling model assumption is z; id Pois (A). (Note, in this question we assume there is no over-reporting of death counts, just under-reporting so yi ≤ ₁.) (a) [2 marks] Assume yi = zi (i 1,..., n). So there is no under-reporting of death counts. Define a prior distribution for A and derive the posterior distribution of A with your chosen prior. (Note, you do not need to provide specific hyperparameter values in your chosen prior assumption). = (b) [3 marks] Now we want to adjust our model for the possibility of under-reporting. The true rate of under-reporting is not known but it is assumed that the reported death count y is at least 80% of the true death count z; (for i = 1,..., n). That is, the under-reporting rate is at most 20%. Give the posterior distribution of λ up to a proportionality constant (that is, ignoring any normalising constant), under this revised model (c) [2 marks] Describe in words how we could use the posterior distribution in (b) to predict the unobserved true death counts zi. In the recent literature, the Poisson distribution has been used to model COVID-19 death counts. Valid estimation of the death rate relies on the availability of accurate data on COVID-19 death counts. In some regions in the world, the accuracy of reported COVID-19 death counts is questionable. We are going to build a Bayesian model to estimate the death rate parameter due to COVID-19 using a Poisson sampling model but also allow for possible under-reporting of death counts. Let y₁, yn be the reported daily death counts for Region A for n different days. Let Z₁, Zn be the true (unreported) death counts, the sampling model assumption is z; id Pois (A). (Note, in this question we assume there is no over-reporting of death counts, just under-reporting so yi ≤ ₁.) (a) [2 marks] Assume yi = zi (i 1,..., n). So there is no under-reporting of death counts. Define a prior distribution for A and derive the posterior distribution of A with your chosen prior. (Note, you do not need to provide specific hyperparameter values in your chosen prior assumption). = (b) [3 marks] Now we want to adjust our model for the possibility of under-reporting. The true rate of under-reporting is not known but it is assumed that the reported death count y is at least 80% of the true death count z; (for i = 1,..., n). That is, the under-reporting rate is at most 20%. Give the posterior distribution of λ up to a proportionality constant (that is, ignoring any normalising constant), under this revised model (c) [2 marks] Describe in words how we could use the posterior distribution in (b) to predict the unobserved true death counts zi.

Answer rating: 100% (QA)

a Assuming there is no underreporting of death counts we can define a prior distribution for the true death counts denoted as X Lets assume a Gamma pr... View the full answer